Basic Properties
The Auslander–Buchsbaum theorem states that every regular local ring is a unique factorization domain.
Every localization of a regular local ring is regular.
The completion of a regular local ring is regular.
If is a complete regular local ring that contains a field, then
- ,
where is the residue field, and, the Krull dimension.
Read more about this topic: Regular Local Ring
Famous quotes containing the words basic and/or properties:
“The man who is admired for the ingenuity of his larceny is almost always rediscovering some earlier form of fraud. The basic forms are all known, have all been practicised. The manners of capitalism improve. The morals may not.”
—John Kenneth Galbraith (b. 1908)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)